Comparing Future Red Tide Scenarios

For this test run, I took the SEDAR Red Grouper stock assessment and used SSMSE to introduce future red tide events in the OM and EM. There were 6 total scenarios:

1. default: the base stock assessment with red tide events in 2005 and 2014.
   
2. red tide random 10: I used a custom function to generate 10 random red tide events in the projected years.
   
3. red tide random 25: I used a custom function to generate 25 random red tide events in the projected years.
   
4. red tide regular 3: I added a red tide event every 3 years.
5. red tide regular 5: I added a red tide event every 5 years.
6. red tide regular 5 mortality 5: I added a red tide event every 5 years and set the OM mortality to 0.5.

Import the results and summary files from the cloud.

Raw Data

Reviewing time series plots

List of the things we can plot with the ts_plot_variable function:

 [1] "year"        "Area"        "Seas"        "Bio_smry"    "SpawnBio"   
 [6] "Recruit_0"   "retainB_1"   "retainN_1"   "retainB_2"   "retainN_2"  
[11] "retainB_3"   "retainN_3"   "retainB_4"   "retainN_4"   "retainB_5"  
[16] "retainN_5"   "deadB_1"     "deadN_1"     "deadB_2"     "deadN_2"    
[21] "deadB_3"     "deadN_3"     "deadB_4"     "deadN_4"     "deadB_5"    
[26] "deadN_5"     "F_1"         "F_2"         "F_3"         "F_4"        
[31] "F_5"         "SPRratio"    "rec_dev"     "raw_rec_dev" "model_run"  
[36] "iteration"   "scenario"   

Here are the time series plots:

Red tide mortality

Figure 1. The fishing mortality of fleet 5 over time. This line plot demonstrates the frequency and magnitude of red tide events in the EM (black) and OM (orange) for each scenario. All 10 iterations of the OM and EM are plotted simultaneously so peaks are representative of the iteration with the highest value and not the overall trend. The OMs have fixed magnitudes and the EMs estimate a F_5 that varies in magnitude but has a median close to the fixed value in the OM.

Table 1. A summary of the Operating Model fleet 5 fishing mortality. These statistics only include values where F_5 > 0.

Scenario	Mean	Standard Dev	Median
red_tide_random_10	0.2	0	0.2
red_tide_random_25	0.2	0	0.2
red_tide_regular_3	0.2	0	0.2
red_tide_regular_5	0.2	0	0.2
red_tide_regular_5_mortality_5	0.5	0	0.5

Table 2. A summary of the Estimated Model fleet 5 fishing mortality. These statistics only include values where F_5 > 0.

Scenario	Mean	Standard Dev	Median
red_tide_random_10	0.146	0.131	0.120
red_tide_random_25	0.161	0.148	0.133
red_tide_regular_3	0.130	0.110	0.113
red_tide_regular_5	0.137	0.104	0.135
red_tide_regular_5_mortality_5	0.413	0.114	0.415

Red tide dead biomass

Figure 2. The biomass of fish killed by red tide over time. This line plot demonstrates the biomass removed by red tide. While fishing mortality is fixed in the OM, the biomass removed can vary depending on the available biomass.

Spawning Stock Biomass

Figure 3. The spawning stock biomass (SSB) over time. These plots best demonstrate the effects of the red tide mortality on the spawning availability, with the increased frequency and magnitude of red tides resulting in lower SSB.

Retained Biomass

Figure 4. The total retained biomass of the fishery over time. This is the sum of all columns starting with “RetainB” so it does not include discards or red tide mortality. This plot demonstrates how impactful high mortality events can reduce catch.

F_1

F_2

F_4

Reviewing derived quantities

Additional time series plots but derived quantities. Below is a list of all the derived quantity variables:

 [1] "Value.SSB"          "Value.Recr"         "Value.SPRratio"    
 [4] "Value.F"            "Value.Bratio"       "Value.ForeCatch"   
 [7] "Value.OFLCatch"     "Value.ForeCatchret" "Value.lnSPB"       
[10] "year"               "model_run"          "iteration"         
[13] "scenario"          

Recruitment

Figure 5. Recruitment over time by scenario. Recruitment is determined by the Beverton-Holt equation using steepness, R0, and SigmaR. Steepness is fixed at 0.99. R0 and SigmaR were estimated in SEDAR 61 and SEDAR 88.

SSB

Figure 6 (same as figure 3). The spawning stock biomass (SSB) over time. These plots best demonstrate the effects of the red tide mortality on the spawning availability, with the increased frequency and magnitude of red tides resulting in lower SSB.

SPR Ratio

Figure 7. The Spawning Potential Ratio (SPR) over time by scenario. This is the spawning output with fishing:the spawning output without fishing so it is a higher value when the reproductive potential is high. SPR tends to spike when there is a red tide event.

B Ratio

Figure 8. The BRatio over time by scenario. The BRatio is the current SSB over the unfished SSB so the value indicates the status of the SSB relative to a unfished scenario. This can be usefull if there is a reference point for BRatio like 0.2 as a cut-off for overfished. Higher frequencies and magnitudes of red tide cause a BRatio less than 0.2 more often.

F

Figure 9. The total fishing mortality over time by scenario. The default scenario indicates that fishing over time has low variability. When Red tide events are introduced, the variability increases drastically as F includes red tide mortality. Since red tide is a by-catch fleet, it is included in this value.

Ratio Time Series

Fishing mortalities

My new method for plotting EM:OM involves creating separate OM and EM data frames, joining them by year, scenario, and iteration, then dividing the EM value/ OM value for every variable. That way when plotted it is truly the EM for each model run, year and iteration divided by the OM from the same year and iteration but one model run. If the om and em value are zero I changed the ratio to 1 because that means that the EM = OM.

10 random red tides

25 random red tides

Red tide every 3 years

Red tide every 5 years

Mortality = 0.5

Figure 10. Each fleet’s fishing mortality ratio (EM:OM) over time by scenario. The line indicates the median and the ribbon is the 25-75% quartiles. F_5 is consistently underestimated, it is more underestimated in future years where there is less data.

F_5

A zoomed in look at just F_5 from the previous plots.

10 random red tides

25 random red tides

Red tide every 3 years

Red tide every 5 years

Mortality = 0.5

Figure 11. Red tide mortality ratio (EM:OM) over time by scenario. The line indicates the median and the ribbon is the 25-75% quartiles. Red tide mortality is consistently underestimated, it is more underestimated in future years where there is less data.

Biomass

10 random red tides

25 random red tides

Red tide every 3 years

Red tide every 5 years

Mortality = 0.5

Figure 12. Biomass ratio (EM:OM) over time by scenario. The line indicates the median and the ribbon is the 25-75% quartiles. Red tide mortality is consistently underestimated, it is more underestimated in future years where there is less data.

Recruitment

Figure 13. Recruitment ratio (EM:OM) over time by scenario. The line indicates the median and the ribbon is the 25-75% quartiles. Recruitment is not over or underestimated, but there are a few outliers where the EM overestimated by 10x.

SSB

Figure 14. SSB ratio (EM:OM) over time by scenario. The line indicates the median and the ribbon is the 25-75% quartiles. SSB is not over or underestimated, but it is more likely to be overestimated, the later years are overestimated. SSB may spike in response to red tide events based on the red_tide_regular_5_mortality_5 scenario.

Terminal Year

Plotting the same ratios as above but by the “time from the terminal year” instead of year. These plots use mean instead of median because there were too many “years until terminal” with no red tide which skewed to 1 and resulted in straight lines. F_5 in all of these plots was a straight line when median was used.

Fishing Mortality

10 random red tides

25 random red tides

Red tide every 3 years

Red tide every 5 years

Mortality = 0.5

Figure 15. Each fleet’s fishing mortality ratio (EM:OM) over the years from terminal year by scenario. The line indicates the mean and the ribbon is the 25-75% quartiles. F_5 is consistently underestimated, there is higher variation where there is less data.

F_5

A zoomed in look at just F_5 from the previous plots.

10 random red tides

25 random red tides

Red tide every 3 years

Red tide every 5 years

Mortality = 0.5

Figure 16. Red tide mortality ratio (EM:OM) over the years from terminal year by scenario. The line indicates the mean and the ribbon is the 25-75% quartiles. F_5 is consistently underestimated, there is higher variation where there is less data.

Biomass

10 random red tides

25 random red tides

Red tide every 3 years

Red tide every 5 years

Mortality = 0.5

Figure 17. Biomass ratio (EM:OM) over the years from terminal year by scenario. The line indicates the mean and the ribbon is the 25-75% quartiles. Red tide mortality is consistently underestimated, it is more underestimated in years where there is less data.

Recruitment

Figure 18. Recruitment ratio (EM:OM) over time by scenario. The line indicates the mean and the ribbon is the 25-75% quartiles. Recruitment is overestimated in the terminal year of the model run.

SSB

Figure 19. SSB ratio (EM:OM) over the years from the terminal year by scenario. The line indicates the mean and the ribbon is the 25-75% quartiles. SSB is underestimated when red tide is introduced, with higher variability in the terminal year of the default model.

Management

Term Plots

default

10 random red tides

25 random red tides

Red tide every 3 years

Red tide every 5 years

Mortality = 0.5

Figure 20. Term plots are meant to be a “short term” (2000-2030) and “long term” (1989-2067) look at a few key parameters from the time series dataset. These plots demonstrate that red tide events correspond with SPR Ratio spikes, and can slowly decrease retained biomass or spawning biomass in the short term. In the long term, there are no trends.

Management Term Plots

default

10 random red tides

25 random red tides

Red tide every 3 years

Red tide every 5 years

Mortality = 0.5

Figure 21. Management Term plots are meant to be a “short term” (2000-2027) and “long term” (1989-2067) look at a few key parameters from the time series dataset. These plots demonstrate that red tide events correspond with SPR Ratio spikes, and can slowly decrease retained biomass or spawning biomass in the short term. In the long term, there are no trends. I tried to add median trend lines for the OM and EM but they aren’t very clear because of how the lines are colored.

Relative Error Plots

Inspired by Wetzel and Punt et al. 2011

I am going to attempt to make their Relative Error Plots.

RE = (E - T) / T

Recruitment

SpawnBio

Com F

Rec F

F_5

Com Catch

Rec Catch

Red Tide Discards

Figure 21. Relative error plots for each variable of interest zoomed in.

Figure 22. Relative error plots of each variable of interest on the same patchwork.

Figure 23. Relative error plots of each variable of interest with fixed x-limits between -2 and 5.

Red Tide Magnitudes and Frequencies

The sums and counts of each red tide treatment to see which are comparable.

# A tibble: 6 × 4
  scenario                       n_years F_5_sum catch_sum
  <chr>                            <int>   <dbl>     <dbl>
1 red_tide_random_10                  10    130.  1781540.
2 red_tide_random_25                  25    356.  3360769.
3 red_tide_regular_3                  17    182.  2009516.
4 red_tide_regular_5                  10    127.  1790006.
5 red_tide_regular_5_mortality_5      10    375.  3427792.
6 default                             NA      0         0 

Table 3. The magnitudes and frequencies of each scenario with the summarized catch to demonstrate scale differences.

Other Explorations

Exploring Recruitment

Recruitment DQ

Recruitment TS

“rec_dev” “raw_rec_dev” “Recruit_0”

rec_dev TS

raw rec_dev TS

Pull data from SS runs

Selectivity Exploration

Selectivity at length (points) with OM line

Selectivity at length (lines) with OM

Zoomed in Selectivity at length

Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
ℹ Please use `linewidth` instead.

Zoomed in Selectivity at length with highlighted line

Selectivity at age (points)

Selectivity at age (lines)

Zoomed in Selectivity at age

Zoomed in Selectivity at age with highlighted line

natage

N at age with OM (dashed)

N at age (lines) in 2017

N at age (points) in 2017

batage

Biomass at age (lines) with OM in 2017

Biomass at age (lines) in 2017

Biomass at age (points) in 2017

catage

Catch at age (lines) in 2017

Catch at age (points) in 2017

Selectivity Exploration Disc

Selectivity at length (points)

Selectivity at length (lines)

Zoomed in Selectivity at length

Zoomed in Selectivity at length with highlighted line

Retention Exploration

Retention one iteration

Retention median

Ro Exploration

Extracted the R0 from SR_LN_R0 from the summary$scalar.

Old versions

Red tide years, biomass ratio, just Com and Rec Retained and Discards

This is the biomass ratios in just the red tide years so the trends are more clear in Fleet 5.

10 random red tides

25 random red tides

Red tide every 3 years

Red tide every 5 years

Mortality = 0.5

F-Ratios over time, All years

10 random red tides

25 random red tides

Red tide every 3 years

Red tide every 5 years

Mortality = 0.5

F/Fmsy Ratio

10 random red tides

25 random red tides

Red tide every 3 years

Red tide every 5 years

Mortality = 0.5

Time Series

Fishing mortalities

10 random red tides

25 random red tides

Red tide every 3 years

Red tide every 5 years

Mortality = 0.5

Figure . F over time by scenario. The line indicates the median for each fleet. When a red tide event happens there is a simultaneous drop in F especially in fleet 4 and a increase in F_4 in the next year. F_1 and F_2 follow a similar but less extreme pattern.

Biomass

10 random red tides

25 random red tides

Red tide every 3 years

Red tide every 5 years

Mortality = 0.5

Figure . Biomass over time by scenario. The line indicates the median for each fleet. When a red tide event happens there is a simultaneous drop in retained biomass and a increase in retained biomass in the next year.

Recruitment

Figure 13. Recruitment ratio (EM:OM) over time by scenario. The line indicates the median and the ribbon is the 25-75% quartiles. Recruitment is not over or underestimated, but there are a few outliers where the EM overestimated by 10x.

SSB